SWAP gate is an essential element of nearest neighbor qubit networks which carry out quantum information processing tasks. The customary way of applying the SWAP gate consists of consecutive probabilistic operations which requires considerable resources. We propose the theoretical design of a structure constructed from linear optical elements on-chip, which applies the SWAP gate deterministically. Using reconfigurable elements, the structure can apply either the SWAP or instead the identity gate. Utilizing components frequently employed in the design and physical implementation of photonic networks on-chip, the structure can be implemented on various platforms. With its compact structure requiring no detectors or ancilla qubits, our design substantially reduces the required resources for the implementation of the SWAP gate.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (
d-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only
d PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.